Walking into the Luxe, I feel even shabbier than usual. I fear those spotless white napkins and wooden counters; I look sidelong at the pricey menu; I sidle off to the side door as soon as possible. Like most of the rest of Spitalfields, this place has gone upmarket and left me behind. Until about a decade ago, it was the Spitz – another restaurant, another bar, another venue. Much loved, and more boho-genteel: I’d come here for electronica, for rock of the post- and mathy variety, and for the occasional off-centre songwriter.

Occasionally I’d come for jazz – something which, as a language, still sits oddly in London’s mouth. It’s not that the city spurns jazz – enough London musicians, venues and festivals give the lie to that. But I feel that sometime it seems a little deracinated here, even in a town where more recent arrivals like reggae and salsa now seem like part of tradition. Supper jazz might be healthy, foyer spaces still welcoming, but outside of grants or outright corporate sponsorship, it’s mostly a tribute to the tenacity and dedication of London’s jazzers that the music keeps its personal, inventive foothold here. The old Spitz was a place which welcomed jazz in plenty of its diverse strands and split-tongued digressions. When you were at a Spitz jazz event, you could feel the music striving, feel its life; and when all of that ended London jazz was diminished.

This picture’s a little too gloomy. There were – and are – other venues, and for those who still want it, the displaced spirit of the Spitz lives on elsewhere as a jazz collective. But it’s heartening that Chaos Theory Promotions (that mobile feast of wide-spanning musical interest, springing from place to place across London) seem to be paying a little homage to old times when they drop their Jazz Market night into the Luxe. Some things stay changed, sadly. I’ve not been here in years, but in Spitz days the music owned the top floor (and a Shoreditch panorama, such as it was). Now it’s down in the basement bar, sharing with the comedy and competing with the toilets: sidelined. Never mind. The Chaos brokers themselves are brimful of enthusiasm, and three jazz trios have come to chat.

If jazz is a language, What?! keep it as handfuls of sentences plunged into a deep baggy pocket, mixed up with anything else they’ve found during the week. Everything in the pocket is regularly hauled up for inspection, to be chucked and scattered casually across a table, just to see how it will fall. The boys certainly aren’t purists, although their taste for locating comfortable licks and riffs in whichever genre they’re toying with does keep you guessing as to how much of what they do is serious. In keeping with this, they’re acting as class clowns tonight. In fetching scarlet dressing-gown and shades, his white-man dreads spilling from a Rasta cap, guitarist Niels Bakx is part-Trustafarian and part-trannie. Bass guitarist Ago Collura, his back turned to the audience, is Reverse Man – a white mask strapped to the back of his head beneath his Tyrolean stovepipe hat, a collar and tie sprouting from the nape of his neck. Having apparently lost a bet, sparky drummer Raphael Lanthaler performs stripped to the waist and down to his underpants (though he’s been allowed to keep his hatful of bright rainbow-dyed feathers as well as his delighted grin).

On record, What?! strut and step like a cool-jazz function band about to be warmed-up and overcome by a sly sense of mischief. Both of their recent singles make a showing tonight – the Brubeck reggae of Tikka Masala (now with extra curlicues from Ago’s bass and curves of wah on the rhythm guitar); a spiked-up, rockier version of Schwaffelen, passing a swaying cats-cradle of jazz and ska touches over and over the tune. This kind of music is what they’re most at home with. It’s not, however, what they’re most drawn to doing. What?! like to stray – prancing into diced-up, chequered rock patterns dominated by the thwack of Raphael’s tom; laying out a sun-stroked Caribbean hiccup for a minute; or suddenly picking up and pelting through some driving motorbike music. Still very young (at an age where anything and everything can be hysterically funny), and still drunk on the musical options that surround them as busy session players and broad listeners, What?! can certainly groove: but they won’t settle.

It’s unclear how many of the band’s disruptions, false halts and oblique quotes are written rather than improvised, but their sense of fun constantly overpowers their artfulness, and every so often their humour dips towards novelty territory. When they slip into a quick strum through Happy Birthday for a friend, it’s warm but a touch too crowd-pleasing. I doubt that What?! wouldn’t care if anyone told them that. An easy-going and sociable band, they’ve invited buddies up to play and clearly thrive on it.

Like a dayglo Tom Waits in his checkered-tablecloth bowler and green tints, the jazz-prankster Moo Clef sits in for a couple of songs. One he plays straight, blowing a fiesta trumpet over a reggae section, fluent and cool-fired. For the other, he adds various sung, rapped and chanted interjections that he tweaks and filters into cartoon oddities via effects pedals. At one point, a chipmunk-voiced cover of Smells Like Teen Spirit takes over, the band smoothly slipping into light-touch Nirvana riffage. The joke wobbles somewhere between Battles and Zappa: disarming romp, or sarcastic cheese. (Or lounge act. Ha.)

It’s a different story when Yasmyn Hendrix and her flower-child headscarf step up to front the trio for Stay With Me. Usually she’s found in unlikely venues, crafting herself castles out of her own vocal loops. Here she plays it straight and soulful, her light but bluesy vocals lounging and skittering over What?!’s skein of tango-funk and Come Together dub-shimmer. For a while, the band sit back and enjoy playing as accompanists. For a while, they stay rooted. They’re good at it. Those quick-cut style shifts and the metafoolery are just part of their choices, not their only option.

Still, in between clear individual pieces the band improvise loosely, and as much with genre as with anything else. They’ll roll out a strolling lunar echo (Raphael sighing and gusting on the drums with near-silent brushstrokes while Niels caresses out wide chords), or crawl through a fragmented, broken-backed jazz ballad that they’ve deconstructed to the point of disintegration. Once they spit out a talking-blues bossa (with Niels on vivid slide guitar), only to refit it midway and produce a tumbling complex skeleton of arpeggiated notes, traveling from Elmore James to Gilberto to Robert Fripp’s League of Gentlemen in a matter of minutes. Towards the end, they throw in a grunge-rock climb complete with punk screaming. Raphael (tonight’s head joker) continually tosses in triggers: false stops and starts, or stalking who-blinks-first contests with Ago.

Again, how much of this is quick coin whipped out of a trick-bag is unclear. What is clear is What?!’s breadth of reference, be it a midsection of shoegazing-summer guitar-echo, a little reggae chip or a mass-less bridging passage of math-rock brewing like a disappearing wreath of mercury fumes. Sometimes their work is a puzzle; sometimes it’s cut-and-shunt. Sometimes, though, it seems as if they’ve scattered themselves out a bit too far, becoming a set of waggling jazz-hands where they should be a breathing, scatting jazz lung. They could do with a little time to breathe in and rethink, maybe.

On first sighting, Macchina del Tempo are raw-boned, hard-faced men. They look like the kind of band that shows up at remote and friendless small-town gigs, purely to prey on other bands. You could imagine them cornering some other, more hapless group in order to swipe and swig their beer in front of them, shake them down for their gig money and then steal their van, all without cracking those stony expressions.

Stocky guitarist Walter Fazio, glowering above his inverted Slayer goatee, looks particularly fearsome, purposeful and frowning – the kind of man who’d grunt one word and unleash hell. Then you see him play. As he smiles, broad and unguarded, while one of his liquid runs of notes hits the spot, then you understand what Macchina del Tempo are really about. Jazz Market regulars, this fusion trio made common cause a few years ago. Two Brits and an Italian, forged in and scarred by the grim working heat of innumerable cover bands, they made a leap to somewhere they could flower.

What Macchina del Tempo provide tonight is a strong contrast to What?!’s permanent state of playful. Effortlessly inventive but tightly-drilled, they roll out four long and muscular pieces of driving jazz-rock ,each with a gritty core which suggests that there might be something to that initial hard-man appearance. If you’re imagining the kind of shrill sterile tech-wank that afflicted jazz-fusion when it gulped down the wrong bits of synthpop and heavy metal at the end of the ‘70s, think again – and think further back. There’s certainly plenty of rock in here, but from the organic end, in which sweat and texture add body and warmth as well as disrupting any shop-fresh sheen.

Certainly Macchina are as much Motorhead as they are Mahavishnu or Metheny (and, given the choice, they appear to be more Rush than Yellowjackets). One of their offerings blends a long-throw fusion funk with creamy jazz metal, a tight seethe of musicality with a laddering, gibbon swing to it. Another starts as a swinging Jimmy Page-meets-Sonny Sharrock hydra – tremendously fluent, ribbed with dissonant slashes but full of tight prog-rock pounces of unison guitar and bass, with a strong rumbling taste of Ace Of Spades (and a final united scurry like La Villa Strangiato).

However, Walter’s persistently inventive guitar playing ensures that the band’s music never boils dry. There might be a bit of Hendrix in his floating horn-wail of lead line, continually playing a push, stroke’n’stretch game with its envelope. There’s probably a pinch of Allan Holdsworth ripple, some dirty Mike Stern blues or Foley McCrearey whumph, an occasional trilling coil of fretboard tapping… whatever there is, it’s subsumed into Walter’s own voice. For the forty minutes he’s onstage, he’s playing almost continually and never once puts a foot wrong. For the full set, he wraps you in the ins and outs of his conversation, his pauses for thought, his gently brooding reflections, frowns and unspoken implications. Guitarists this compelling and fertile are rare – and they’re a pleasure to encounter.

From the start, it’s also been clear that Macchina have an utter mastery of the flexible groove. While drummer Mick Claridge can certainly swing, it’s only part of his vocabulary as the band drive and chivvy through their smooth shifts of time and tempo. On bass guitar, Jamie McKenzie plays neither the great soloist nor the staid, conservative backliner. Instead he firmly unzips the chords in all their glory, then fingers his way around and across the scales in a continous springy roam. A dextrous fretted fingerstylist, he knows where every note needs to go. His playing creates a webbing of involved, swung-baroque bass-line, over which Walter’s guitar can flicker like a sly chameleon whenever it needs to. Mick subtly supports the arc; swirls under it, drums cruising and lifting like a river-rise.

They’re certainly making an impact – around me, bodies rapidly lose their reluctance, peeling up from the Luxe’s dark faux-leather sofas to sway and wave to the Macchina percolations. A third piece, though it starts with a crabby rock sidle strangely similar to You Really Got Me, soon turns into electric-chicken jazz funk. Mick slides greasy rhythms from hand to hand even as he pins the piece to the floor, a human nail-gun. For the last in their foursome of amplified groove, the band’s funk turns a little Mahavishnu: full of tensing stops, bullish balance and hot scraps sliding unregarding from that smouldering guitar. Even now, deep into their set, the three Macchina men seem transformed by their playing. Seeing those tough faces softened and gentled into something resembling reverence – it does the heart good.

What?! have the playful end of things covered tonight. Macchina del Tempo have so convincingly laid claim to solidity and substance that they’d be tough to follow with something similar. It falls to A Sweet Niche, then, to stagger splay-armed along the edge; to rake their nails down the rough wall of art and shout the appropriate odds.

Ben Handysides drums with dainty motions but powerful strikes. He looks like a handsome public-school rugger star who’s thinking about becoming a poet; he can play jazz, folk, progressive rock, kletzmer and sundry permutations of all of those and more. This makes him a shoo-in for A Sweet Niche when they play live. While they’ve already got an established drummer for composing and recording, he lives, rather disobligingly, far off in Cornwall (where he can presumably maintain the freshness required for their studio sessions). Everyone else in the band besides Ben seems to have intense sidelines in film, or theatre, or the spiky world of contemporary classical. Perhaps this explains the open-marriage, flyaway feel of the band; and why Ben currently seems like a blond bridge linking the two remaining poles of A Sweet Niche together.

One of these two poles is Oliver Sellwood, on baritone sax. He’s a fluid rippling player (with plenty of bassy skronk in him whenever he needs it) and he’s as well turned out as his playing: neat haircut, neat glasses, unflappable demeanour. He can blow like a demon, but he delivers these storms coolly and professorial, as if chatting from a podium. The other pole is on the other side of Ben and looks as if he’ll rattle himself to bits at any moment. In his agony-scarlet sweat top, Keir Cooper is spindly and driven; bristle-bearded, and playing a guitar as if someone will nail him to it at set’s end. Everything about him screams “art lifer”. He’s the filmmaker. He probably sleeps once or twice every five years, if someone else talks him into it.

A Sweet Niche cast off with a clutch of snaking instrumental wiggles. Oliver’s baritone sax tattoo soon settles into a blaring drone, around which Ben casts up a ticking construction set before the band blaze up into distortion. Keir is clearly going to be the splinter in the jam – his face crumples into walnut creases as he drives shattered howls out of his guitar. Ben looks loose in comparison, his drumsticks dangling like plucked lilies. Oliver disregards them both, ripping off a sax solo as if he was wrenching a seam from a jacket: it’s a little Arabian in tone, a reproving and arrogant ripple of grace above the chaos, of which there’s plenty more to come.

Their second salvo, Eye Music II is crash noise from the off. Their third begins as a kind of minimalist ska, then becomes Yaketty-Yak re-imagined for math-rockers. After Ben delivers a burst of horse-clopping rimshots, they break for another swirl of Arabian saxophone, heavy on the romance, before heading back towards the ska armed with hammer-swipes of noise. To top it off, the coda is a lullaby pop tune.

As a band – or, perhaps, as a spasm – A Sweet Niche seem to crouch somewhere between John Zorn (in his more impish Naked City moods) and the wracked, Maoist judders of English free jazz. Moments where a passage of brittle swing mutates into a kind of thrash samba could be put down to dark humour, but it’s difficult to calculate the shape of the band’s intent when a cheerful passage of saxophone sleaze is overtaken by screeching guitar alarm and then a taut, distant game of musical tag as Keir and Oliver dot each other with single notes and with silence.

It’s tricky to pin down whether what they do is political, or disruptive for its own sake, or just a natural expression of brain hiccups; or whether all of these options are equally valued or dismissed. Besides their wary body language – which could be a deceptive feint anyway – they give little away personally. There are no arcane jokes at the microphone, and few wacky titles (although the choppy ta-ta-ta and carousel echos of Bananagirl inspire even more confusion, as if Bagpuss had joined Slayer).

Ultimately A Sweet Niche’s aim seems to be to blow their education out of their minds, like a bolus of brain-snot. Chunks of structure regularly whiz past our ears (Oliver, in particular, has a knack for hurling fervent and compressed musical dialogue) while Keir is ceaseless in shaking off his thoughts as an urgent, committed racket. At one point, following a particularly intense bit of guitar wringing, he blinks with astonishment. For a few seconds, he looks relieved, with a surprised smile and the hint of shy laughter fluttering round his chops, and a “where did that come from?” shrug lifting his arms. As they head towards the end of their set, though, their disruptive peace-destroying turns into a dotted bounce. Bit by bit, they’re turning to a dance even if at the next song they’ll be trying to squash us against the wall with ripped slices of metallic thrash-hop.

They end with a thunderous, purging blast through Duodecimal. Then, bizarrely, they’re back for an encore, augmented by Chloe Herington (the unflappable reedswoman from Chrome Hoof, VALVE and Knifeworld) who suddenly pops up to moonlight and to add a new factor to the band’s unruly chemistry. There’s plenty of muttering, subtle stares and subliminal eyebrow gestures before they get started. It’s unclear whether they’re cueing each other, playing chicken or attempting some kind of disguised wink-murder.

Just as I’m losing interest, they reel out a tremendous length of jazz-thrash-turned-sludge-metal. Her alto sax hovering, Chloe stays silent for most of it before jerking into place right at the pell-mell coda. She blows ten or fifteen seconds of twisting Coltrane overblowing over the roar, and then everything crashes to a halt. The night’s over, and so is A Sweet Niche’s psychological shell game. The strains and strange focusses slough away like last month’s bandages: with the instruments down, they’re suddenly warm with each other.

Ten minutes later, sleepy and stumbling, I’m making my way south-west of Spitalfields and I’m ever so slightly lost. Trying to find the tube, I’m wandering past the cluster of City skyscrapers by Bishopsgate – pushy assertions, half-formed nubbins and works-in-progress, garlanded by lights: and the finished statements, shoved heavenwards. Appropriate really.

Around my midnight bleariness (and as I’m passing the arrested concrete stump of the Pinnacle building, humiliated and frozen by market forces) I’m thinking dimly about language again, about tunes and stutters and babels and temporary silences. I don’t come to a conclusion, but as the last echoes of the gig swirl away in my mind I’m feeling glad that this part of town’s got some of its more unusual dialogues back.

All right, they suckered me. I thought that What?! were starting a gimmick tradition of rolling out cute singles named after foodstuffs. A natural suspicion – their debut single had the crowd-pleasing title of Tikka Masala. Actually, it turns out that “schwaffelen” is Dutch slang, and refers to a man repeatedly bouncing his semi-erect penis off assorted objects (ranging from someone else’s cheekbone to the side of the Taj Mahal). Handy phrase – consider me educated. I’ve been saved some embarrassment the next time I’m snacking in Amsterdam, but have been left with a delightful image of waffles-and-cream that I now need to bleach from my mind. Thanks for that.

What?! remain the kind of supple instrumental trio that gives slick a good name – guitar, bass guitar, drums and a thorough versing in everything out there which grooves. They also own a not-so-secret knowledge of plenty of things which don’t groove but which do lurk, puzzle over things and then jump out at you. But they’ve yet to really show their other teeth: those rougher, odder inspirations they claim to get from Zappa, Dub Trio and Mr Bungle. So far, they’ve been more about delicate sunlit jazzy chords and walks, clean deft swing, and plenty of space. You get the feeling that they could do anything with their material – as soon as they wanted to – and that they’re fencing with expectations. It’s just that it’s still not clear when they’re going to stop fencing and start carving.

As much as you might want them to get nastier, Schwaffelen doesn’t show What?! chucking away any of their finesse in favour of skronk or sludge. If they’re stepping towards a spikier direction, they’re starting subtle – taking some sour art-rock patterns and passing them back and forth through the smooth-jazz filter. As with Tikka Masala, there’s a hint of Take 5 in the gently precise stops and feints as a bossa nova is displaced and reshuffled into math-rock spikes. But the truth is that, in spite of the cock-bouncing title, What?! keep their all-things-to-all-men decorum throughout – even when hitting the distortion pedals.

If you’re hoping for some upheaval – something like the obsessive rhythmic knotting of Battles, say, or the disruptive slice-and-dice of Naked City – you’re in the wrong place. Schwaffelen’s flexing sections do include a flawless switch into driving rock as guitarist Niels Bakx starts blasting away and Agostino Collura’s nimble bass drops its funky slither and locks down into root-note pummeling. But this is more an exercise in clever distraction. Even as Raphael Lanthaler drums along at motorway-punk velocity, the whole band are keeping an eye on the little loping twists of the original rhythm: as it ghosts on underneath, they’ll lock seamlessly back into it whenever they choose. Even the texture phase (in which Niels seems to be channeling the sparse echo-spangled touch of Andy Summers) adds some extra breadth but no questioning depth or disruption.

Perhaps it doesn’t matter – whatever else they might or might not do, What?! remain supremely elegant puzzlers. But it still feels as if there’s much more to them. The Key Ness remix of Schwaffelen is barely half the length of the original, but during its stay it chops, rewinds and pans the original riffs around a gastric roller-coaster of sub-bass and boiling P-Funk synth. Along the way, it twirls past Alice Coltrane harp cascades, brief bursts of classical soul orchestras, wind-tossed shouts from hip-hop MCs and gutsy flowerings of Spanish guitar. It sounds more like what must go on in the trio’s heads – what they must listen to on iPods, gulp down from session to session, or coast by on the bus.

One last thing, going back to the original track… As it snaps to a halt and telescopes away, with a quick twist-and-growl, those push-pulling rhythms leave you in a state of expectation. There’s a moment of hover. Then there’s several messy, prolonged seconds of the most horrendous splurging musical spoff-noise you can imagine. Maybe it’s a surprise, a pancaked blast-beat hurled out by Raphael to be crushed flat in the mix. Whatever it is, it’s a Zappa-style kiss-off. Perhaps I’ve been unfair to What?!. They did finally deliver that dirty splatter.

Sometimes you can come across simple treasures hiding in the backroom. Dutch guitarist Niels Bakx, Sicilian drummer Raphael Lanthaler and Tyrolean bass player Agostino Collura are part of that under-appreciated swirl of humble, talented international musicians who fly in, settle down and quietly underpin bands in London, as in many big cities. People like these plug away behind the people with the big ideas and the knack for fronting. They’re the ones who finesse the roughness, who add the musical depth and the polish which brings shine and sophistication to performance. And sometimes, they secretly bring more.

Individually, each of these three have clearly got the chops and the temperament to keep themselves in demand with songwriters (Agostino plays with Anna Waldmann’s band The Cry Baby, Niels and Raphael back Charlotte Eriksson in The Glass Child), embedded in soul collectives (Agostino’s work with Retrospective For Love) and driving mixed groove-band (Raphael’s Snail Trail). Together, though, Niels, Raphael and Agostino are something else.

As What?!, they’re an assured and formidable unit; an airy, confident groove-trio audibly revelling in their flexibility and their knack for carefully-sprung timing. On spec, there’s nothing particularly unusual in what they do. Enough years spent plugging away at sessions and keeping punters happy with funk, soul, jazz and reggae tunes have made them experts in warm, sunny, foot-moving musicality: but it’s what’s beyond the blueprint that’s interesting.

Their debut single Tikka Masala (named, consciously or not, after a meal made up on the spot to keep British customers happy) is a sweet-natured hall-of-mirrors groove, light and slinky. There’s reggae in it, thanks to Raphael’s displaced bass drum taps, his tight-tuned tom rattles and Niel’s skinny-supple rhythm guitar. There’s funk in the warm spaces between strokes and beats. There’s jazz in everything, from the little golden runs of licks to the turnarounds to the feel that the rhythms are to be flung from hand to hand, danced over, teased and tag-teamed around. There are subtle refractions, interruptions of rhythm and key, that make you think briefly of progressive rock at its least bombastic and most aware. There are also flares of hard rock when all three musicians line up under a suddenly roaring guitar and suddenly start jabbing together ahead of the beat.

What’s really special about it is their complete control over the music. Their discipline is absolute but relaxed, with the feel that at any time they could shift rhythm, speed, genre back and forth in a moment, and yet not drop a single thing along the way. There are no self-conscious cut-ups in What?!’s music – no need to deconstruct. Why should there be when they’re masters of structure? – so much that if you flipped Tikka Masala around and spun it backwards it would keep every bit of its symmetry and bounce. For a demonstration of this, play the bonus track Alasam Akkit as that’s exactly what that is – a backwards-play of the A-side which sounds almost as good as the forwards version. A backwards-play which you can still dance to. Remarkable.

Exactly what this leads to, I’m not sure. Perhaps the outcome is that What?! set themselves up as a twenty-first century Sly and Robbie-plus-one. Perhaps they remain a supremely-accomplished hobby band, something which the trio engage in when they’re not otherwise employed keeping other people happy. Or do they push ahead as self-sufficient instrumentalists, seeing how far they can push, stretch and double-feint their masterful musicality? The only thing I can be sure of is that, whenever they do get together, all ways – for those moments – are open; and it’s tremendously refreshing.